Cutting elements comprising waveforms and related tools and methods

ABSTRACT

Cutting elements for earth-boring tools may include a polycrystalline, superabrasive material secured to an end of a substrate. The polycrystalline, superabrasive material may include a first transition surface and a second transition surface. A waveform may extend around a circumference of the second transition surface, a surface of the waveform tapered toward from the substrate and extending radially from the second transition surface toward the central axis. The surface of the waveform may extend from the second transition surface to a planar surface of the polycrystalline located at a same distance from the substrate as troughs of the waveform surface, the planar surface oriented perpendicular, and located proximate, to the central axis.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.15/584,943, filed May 2, 2017, now U.S. Pat. No. 10,400,517, issued Sep.3, 2019, the disclosure of which is incorporated herein in its entiretyby this reference.

FIELD

This disclosure relates generally to cutting elements for earth-boringtools, to earth-boring tools carrying such cutting elements, and torelated methods. More specifically, disclosed embodiments relate tocutting elements for earth-boring tools that may better resist impactdamage, induce beneficial stress states within the cutting elements, andimprove cooling of the cutting elements.

BACKGROUND

Some earth-boring tools for forming boreholes in subterraneanformations, such as, for example, fixed-cutter earth-boring rotary drillbits (also referred to as “drag bits”) and reamers, include cuttingelements comprising superabrasive, conventionally polycrystallinediamond compact (PDC) cutting tables mounted to supporting substratesand secured to the rotationally leading portions of blades. The cuttingelements are conventionally fixed in place, such as, for example, bybrazing the cutting elements within pockets formed in the rotationallyleading portions of the blades. Because formation material removalexposes the formation-engaging portions of the cutting tables to impactsagainst the subterranean formations, they may chip, which dulls theimpacted portion of the cutting element or even spall, resulting in lossof substantial portions of the table. Continued use may wear away thatportion of the cutting table entirely, leaving a completely dull surfacethat is ineffective at removing earth material.

BRIEF SUMMARY

In some embodiments, cutting elements for earth-boring tools may includea substrate and a polycrystalline, superabrasive material secured to anend of the substrate. The polycrystalline, superabrasive material mayinclude a first transition surface extending in a direction oblique to acentral axis of the substrate, a second transition surface extending ina second direction oblique to the central axis, the second directionbeing different from the first direction, and a curved, stress-reductionfeature located on the second transition surface.

In other embodiments, earth-boring tools may include a body and acutting element secured to the body. The cutting element may include asubstrate and a polycrystalline, superabrasive material secured to anend of the substrate. The polycrystalline, superabrasive material mayinclude a first transition surface extending in a direction oblique to acentral axis of the substrate, a second transition surface extending ina second direction oblique to the central axis, the second directionbeing different from the first direction, and a curved, stress-reductionfeature located on the second transition surface.

In still other embodiments, methods of making cutting elements forearth-boring tools may involve shaping a polycrystalline, superabrasivematerial to include: a first transition surface extending in a directionoblique to a central axis of the substrate; a second transition surfaceextending in a second direction oblique to the central axis, the seconddirection being different from the first direction; and a curved,stress-reduction feature located on the second transition surface. Thepolycrystalline, superabrasive material may be secured to a substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

While this disclosure concludes with claims particularly pointing outand distinctly claiming specific embodiments, various features andadvantages of embodiments within the scope of this disclosure may bemore readily ascertained from the following description when read inconjunction with the accompanying drawings, in which:

FIG. 1 is a perspective view of an earth-boring tool;

FIG. 2 is a perspective view of an embodiment of a cutting elementusable with the earth-boring tool of FIG. 1;

FIG. 3 is a side view of a portion of the cutting element of FIG. 2;

FIG. 4 is a perspective view of another embodiment of a cutting elementusable with the earth-boring tool of FIG. 1;

FIG. 5 is a close-up perspective view of a portion of the cuttingelement of FIG. 4;

FIG. 6 is a perspective view of yet another embodiment of a cuttingelement usable with the earth-boring tool of FIG. 1;

FIG. 7 is partial cutaway perspective view of still another embodimentof a cutting element usable with the earth-boring tool of FIG. 1; and

FIG. 8 is a cross-sectional side view of a container usable for formingcutting elements in accordance with this disclosure.

DETAILED DESCRIPTION

The illustrations presented in this disclosure are not meant to beactual views of any particular cutting element, earth-boring tool, orcomponent thereof, but are merely idealized representations employed todescribe illustrative embodiments. Thus, the drawings are notnecessarily to scale.

Disclosed embodiments relate generally to cutting elements forearth-boring tools that may better resist impact damage, inducebeneficial stress states within the cutting elements, and improvecooling of the cutting elements. More specifically, disclosed areembodiments of cutting elements that may include multiple transitionsurfaces proximate a periphery of the cutting elements, at least onecurved, stress-reduction feature located on one or more of thetransition surfaces, and an optional recess extending from a radiallyinnermost transition surface back toward a substrate of the respectivecutting element.

The term “earth-boring tool,” as used herein, means and includes anytype of bit or tool used for drilling during the formation orenlargement of a wellbore in a subterranean formation. For example,earth-boring tools include fixed-cutter bits, roller cone bits,percussion bits, core bits, eccentric bits, bicenter bits, reamers,mills, drag bits, hybrid bits, and other drilling bits and tools knownin the art.

As used herein, the term “superabrasive material” means and includes anymaterial having a Knoop hardness value of about 3,000 Kgf/mm² (29,420MPa) or more. Superabrasive materials include, for example, diamond andcubic boron nitride. Superabrasive materials may also be characterizedas “superhard” materials.

As used herein, the term “polycrystalline material” means and includesany structure comprising a plurality of grains (i.e., crystals) ofmaterial that are bonded directly together by inter-granular bonds. Thecrystal structures of the individual grains of the material may berandomly oriented in space within the polycrystalline material.

As used herein, the terms “inter-granular bond” and “interbonded” meanand include any direct atomic bond (e.g., covalent, metallic, etc.)between atoms in adjacent grains of superabrasive material.

The term “sintering,” as used herein, means temperature driven masstransport, which may include densification and/or coarsening of aparticulate component. For example, sintering typically involvesshrinkage and removal of at least some of the pores between the startingparticles, accompanied by part shrinkage, combined with coalescence andbonding between adjacent particles.

As used herein, the term “tungsten carbide” means any materialcomposition that contains chemical compounds of tungsten and carbon,such as, for example, WC, W₂C, and combinations of WC and W₂C. Tungstencarbide includes, for example, cast tungsten carbide, sintered tungstencarbide, and macrocrystalline tungsten carbide.

Referring to FIG. 1, a perspective view of an earth-boring tool 100 isshown. The earth-boring tool 100 may include a body 102 having cuttingelements 104 secured to the body 102. The earth-boring tool 100 shown inFIG. 1 may be configured as a fixed-cutter drill bit, but otherearth-boring tools having cutting elements 104 secured to a body may beemployed, such as, for example, those discussed previously in connectionwith the term “earth-boring tool.” The earth-boring tool 100 may includeblades 106 extending outward from a remainder of the body 102, with junkslots 108 being located rotationally between adjacent blades 106. Theblades 106 may extend radially from proximate an axis of rotation 110 ofthe earth-boring tool 100 to a gage region 112 at a periphery of theearth-boring tool 100. The blades 106 may extend longitudinally from aface 114 at a leading end of the earth-boring tool 100 to the gageregion 112 at the periphery of the earth-boring tool 100. Theearth-boring tool 100 may include a shank 116 at a trailing end of theearth-boring tool 100 longitudinally opposite the face 114. The shank116 may have a threaded connection portion, which may conform toindustry standards (e.g., those promulgated by the American PetroleumInstitute (API)), for attaching the earth-boring tool 100 to a drillstring.

The cutting elements 104 may be secured within pockets 118 formed in theblades 106. Nozzles 120 located in the junk slots 108 may directdrilling fluid circulating through the drill string toward the cuttingelements 104 to cool the cutting elements 104 and remove cuttings ofearth material. The cutting elements 104 may be positioned to contact,and remove, an underlying earth formation in response to rotation of theearth-boring tool 100 when weight is applied to the earth-boring tool100. For example, cutting elements 104 in accordance with thisdisclosure may be primary or secondary cutting elements (i.e., may bethe first or second surface to contact an underlying earth formation ina given cutting path), and may be located proximate a the rotationallyleading surface 122 of a respective blade 106 or may be secured to therespective blade 106 in a position rotationally trailing therotationally leading surface 122.

FIG. 2 is a perspective view of an embodiment of a cutting element 130usable with the earth-boring tool 100 of FIG. 1. The cutting element 130may include a substrate 132 and a table of polycrystalline,superabrasive material 134 secured to an end 136 of the substrate 132.More specifically, the polycrystalline, superabrasive material 134 maybe a polycrystalline diamond compact (PDC). The substrate 132 may begenerally cylindrical in shape. For example, the substrate 132 mayinclude a curved side surface 138 extending around a periphery of thesubstrate 132 and end surfaces 140 and 142. The end surfaces 140 and 142may have a circular or oval shape, for example. The end surfaces 140 and142 may be, for example, planar or nonplanar. For example, the endsurface 140 forming an interface between the substrate 132 and thepolycrystalline, superabrasive material 134 may be nonplanar. In someembodiments, the substrate 132 may include a chamfer transitioningbetween the side surface 138 and one or more of the end surfaces 140 and142, typically between side surface 138 and end surface 142. Thesubstrate 132 may have a central axis 150 extending parallel to the sidesurface 138 through geometric centers of the end surfaces 140 and 142.The substrate 132 may include hard, wear-resistant materials suitablefor use in a downhole drilling environment. For example, the substrate132 may include metal, metal alloys, ceramic, and/or metal-ceramiccomposite (i.e., “cermet”) materials. As a specific, nonlimitingexample, the substrate 132 may include a cermet including particles oftungsten carbide cemented in a metal or metal alloy matrix.

The polycrystalline, superabrasive material 134 may include aninterfacial surface 144 abutting, and secured to, the end surface 140 ofthe substrate 132. The polycrystalline, superabrasive material 134 maybe generally disc-shaped, and may include a side surface 146 extendinglongitudinally from the interfacial surface 144 away from the substrate132. The side surface 146 may be curved, and may be, for example, flushwith the side surface 138 of the substrate 132.

The polycrystalline, superabrasive material 134 may include a firsttransition surface 148 extending from the side surface 146 away from thesubstrate 132. The first transition surface 148 may have a frustoconicalshape, and may comprise what is often referred to in the art as a“chamfer” surface. The first transition surface 148 may extend away fromthe substrate 132 in a first direction oblique to the central axis 150of the substrate 132. The first transition surface 148 may extendradially from the side surface 146 at the periphery of thepolycrystalline, superabrasive material 134 inward toward the centralaxis 150. In some embodiments, the polycrystalline, superabrasivematerial 134 may lack the side surface 146, such that the firsttransition surface 148 may begin at an intersection (e.g., an edge) withthe interfacial surface 144 located adjacent to the end surface 140 ofthe substrate 132.

The polycrystalline, superabrasive material 134 may further include asecond transition surface 152 extending from the first transitionsurface 148 away from the substrate 132. The second transition surface152 may extend away from the substrate 132 in a second direction obliqueto the central axis 150 of the substrate 132. The second direction inwhich the second transition surface 152 extends may be different fromthe first direction in which the first transition surface 148 extends.The second transition surface 152 may extend radially from the firsttransition surface 148 at the radially innermost extent thereof inwardtoward the central axis 150. For example, the second transition surface152 may extend radially inward more rapidly than the first transitionsurface 148.

In some embodiments, such as that shown in FIG. 2, the polycrystalline,superabrasive material 134 may include a cutting face 154 extending fromthe second transition surface 152 radially inward to the central axis150. The cutting face 154 may extend, for example, in a directionperpendicular to the central axis 150. Each of the first transitionsurface 148, the second transition surface 152, and the cutting face 154may have a cross-sectional shape at least substantially similar to,though smaller in a radial extent than, a cross-sectional shape of theside surfaces 138 and 146 of the substrate 132 and the polycrystalline,superabrasive material 134. In some embodiments, the cutting face 154may exhibit a different degree of roughness than a remainder of theexposed surfaces of the polycrystalline, superabrasive material 134. Forexample, the cutting face 154 may be rougher than (e.g., may be polishedto a lesser degree or with a less fine polish) the remainder of theexposed surfaces of the polycrystalline, superabrasive material 134.More specifically, a difference in surface roughness between the cuttingface 154 and the remainder of the exposed surfaces of thepolycrystalline, superabrasive material 134 may be, for example, betweenabout 1 μin Ra and about 30 μin Ra. Ra may be defined as the arithmeticaverage of the absolute values of profile height deviations from themean line, recorded within an evaluation length. Stated another way, Rais the average of a set of individual measurements of a surface's peaksand valleys. As a specific, nonlimiting example, the difference insurface roughness between the cutting face 154 and the remainder of theexposed surfaces of the polycrystalline, superabrasive material 134 maybe between about 20 μin Ra and about 25 μin Ra. As continuing examples,a surface roughness of the cutting face 154 may be between about 20 μinRa and about 40 μin Ra, and a surface roughness of the remainder of theexposed surface of the polycrystalline, superabrasive material 134 maybe between about 1 μin Ra and about 10 μin Ra. More specifically, thesurface roughness of the cutting face 154 may be, for example, betweenabout 20 μin Ra and about 30 μin Ra, and the surface roughness of theremainder of the exposed surface of the polycrystalline, superabrasivematerial 134 may be, for example, between about 1 μin Ra and about 7 μinRa. As specific, nonlimiting examples, a surface roughness of thecutting face 154 may be between about 22 μin Ra and about 27 μin Ra(e.g., about 25 μin Ra), and a surface roughness of the remainder of theexposed surface of the polycrystalline, superabrasive material 134 maybe between about 1 μin Ra and about 5 μin Ra (e.g., about 1 μin Ra). Thechange in direction from the second transition surface 152 to thecutting face 154, and the optional change in roughness in certainembodiments, may cause cuttings produced by the cutting element 130 tobreak off, acting as a chip breaker.

By increasing the number of transition surfaces relative to a cuttingelement with a single chamfer, the cutting element 130 may increase thetime over which an impulse resulting from contact with an earthformation may act on the cutting element. As a result, the cuttingelement 130 may reduce peak collision force, reducing impact and chipdamage and increasing the useful life of the cutting element 130.

The cutting element 130 may further include a curved, stress-reductionfeature 156 located on the second transition surface 152. The curved,stress-reduction feature 156 may be sized and shaped to induce abeneficial stress state within the polycrystalline, superabrasivematerial 134. More specifically, the curved stress-reduction feature 156may reduce the likelihood that tensile stresses will occur, and mayreduce the magnitude of any tensile stresses that appear, in thepolycrystalline, superabrasive material 134. As shown in FIG. 2, thecurved, stress-reduction feature 156 may be a radiusing of the secondtransition surface 152 itself in some embodiments.

FIG. 3 is a side view of a portion of the cutting element 130 of FIG. 2.As shown in FIGS. 2 and 3, the first transition surface 148 may be achamfered surface in some embodiments. For example, the first transitionsurface 148 may extend at a constant slope from the side surface 146toward the central axis 150 (see FIG. 2). More specifically, a firstacute angle θ₁ between the first transition surface 148 and the centralaxis 150 (see FIG. 2) may be, for example, between about 30° and about60°. As a specific, nonlimiting example, the first acute angle θ₁between the first transition surface 148 and the central axis 150 (seeFIG. 2) may be between about 40° and about 50° (e.g., about 45°). Afirst thickness T₁ of the first transition surface 148 as measured in adirection parallel to the central axis 150 (see FIG. 2) may be, forexample, between about 5% and about 20% of a total thickness T of thepolycrystalline, superabrasive material 134 as measured in the samedirection. More specifically, the first thickness T₁ of the firsttransition surface 148 may be, for example, between about 7% and about15% of the total thickness T of the polycrystalline, superabrasivematerial 134. As a specific, nonlimiting example, the first thickness T₁of the first transition surface 148 may be between about 8% and about12% (e.g., about 10%) of the total thickness T of the polycrystalline,superabrasive material 134. The first thickness T₁ of the firsttransition surface 148 may be, as another example, between about 0.014inch and about 0.018 inch. More specifically, the first thickness T₁ ofthe first transition surface 148 may be, for example, between about0.015 inch and about 0.017 inch. As a specific, nonlimiting example, thefirst thickness T₁ of the first transition surface 148 may be about0.016 inch.

The second transition surface 152 may be a truncated dome shape in someembodiments, such as that shown in FIGS. 2 and 3. For example, a slopeof the second transition surface 152 may change at least substantiallycontinuously, and at an at least substantially constant rate, from thefirst transition surface 148 to the cutting face 154. More specifically,a radius of curvature R₂ of the second transition surface 152 may be,for example, between about 0.02 inch and about 0.13 inch. As a specific,nonlimiting example, the radius of curvature R₂ of the second transitionsurface 152 may be, for example, between about 0.06 inch and about 0.1inch (e.g., about 0.08 inch). A second thickness T₂ of the secondtransition surface 152 as measured in a direction parallel to thecentral axis 150 (see FIG. 2) may be greater than the first thickness T₁of the first transition surface 148 and may be, for example, betweenabout 5% and about 50% of the total thickness T of the polycrystalline,superabrasive material 134 as measured in the same direction. Morespecifically, the second thickness T₂ of the second transition surface152 may be, for example, between about 15% and about 45% of the totalthickness T of the polycrystalline, superabrasive material 134. As aspecific, nonlimiting example, the second thickness T₂ of the secondtransition surface 152 may be between about 20% and about 35% (e.g.,about 30%) of the total thickness T of the polycrystalline,superabrasive material 134. The second thickness T₂ of the secondtransition surface 152 may be, as another example, between about 0.01inch and about 0.05 inch. More specifically, the second thickness T₂ ofthe second transition surface 152 may be, for example, between about0.02 inch and about 0.04 inch. As a specific, nonlimiting example, thesecond thickness T₂ of the second transition surface 152 may be about0.03 inch.

FIG. 4 is a perspective view of another embodiment of a cutting element160 usable with the earth-boring tool 100 of FIG. 1. In someembodiments, such as that shown in FIG. 4, a second transition surface162 may not curve as it extends from the first transition surface 148 tothe cutting face 154. For example, a slope of the second transitionsurface 162 may be constant as it extends in a direction oblique to thecentral axis 150 from the side surface 146 to the cutting face 154.

As shown in FIG. 4, the curved, stress-reduction feature 156 may includea pattern of bumps 164 located on, and protruding from, the secondtransition surface 162. A perimeter of the bumps 164 may be of anyshape, such as, for example, circular, triangular, quadrilateral, etc.As a specific, nonlimiting example, the perimeter of a given bump 164shown in FIG. 4 as viewed in a plane tangent to the second transitionsurface 152 at a geometric center of the given bump 164 may be generallycircular. Each bump 164 may bulge outward from the second transitionsurface 152, and may be arcuate in shape as it extends away from thesecond transition surface 152. A maximum distance D between points at aperiphery of a given bump 164 may be, for example, between about 90% andabout 100% of a minimum length L of the second transition surface 152measured between its intersection with the side surface 146 or theinterfacial surface 144 and the cutting face 154. More specifically, themaximum distance D between points at the periphery of a given bump 164may be, for example, between about 95% and about 100% of the minimumlength L of the second transition surface 152 measured between itsintersection with the side surface 146 or the interfacial surface 144and the cutting face 154. As a specific, nonlimiting example, themaximum distance D between points at the periphery of a given bump 164may be about 100% of the minimum length L of the second transitionsurface 152 measured between its intersection with the side surface 146or the interfacial surface 144 and the cutting face 154. The maximumdistance D between points at the periphery of a given bump 164 may be,for example, between about 0.001 inch and about 0.02 inch. Morespecifically, the maximum distance D between points at the periphery ofa given bump 164 may be, for example, between about 0.005 inch and about0.015 inch. As a specific, nonlimiting example, the maximum distance Dbetween points at the periphery of a given bump 164 may be between about0.008 inch and about 0.012 inch (e.g., about 0.01 inch).

A frequency at which the bumps 164 may be positioned around the secondtransition surface 152 may be, for example, between about one every 90°and about ten every 90°. More specifically, the frequency at which thebumps 164 may be positioned around the second transition surface 152 maybe, for example, between about two every 90° and about eight every 90°.As a specific, nonlimiting example, the frequency at which the bumps 164may be positioned around the second transition surface 152 may be, forexample, between about three every 90° and about seven every 90° (e.g.,about five every 90°). A total number of bumps 164 located around thecircumference of the second transition surface 152 may be, for example,between about four and about 40. More specifically, the total number ofbumps 164 located around the circumference of the second transitionsurface 152 may be, for example, between about eight and about 32. As aspecific, nonlimiting example, the total number of bumps 164 locatedaround the circumference of the second transition surface 152 may be,for example, between about 12 and about 28 (e.g., about 20).

FIG. 5 is a close-up perspective view of a portion of the cuttingelement 160 of FIG. 4. As shown in FIGS. 4 and 5, the second transitionsurface 152 may be a chamfered surface in some embodiments. For example,the second transition surface 152 may extend at a constant slope fromthe side surface 146 toward the central axis 150 (see FIG. 4). Morespecifically, a second acute angle θ₂ between the second transitionsurface 152 and the central axis 150 (see FIG. 4) may be, for example,between about 30° and about 89°. As a specific, nonlimiting example, thefirst acute angle θ₁ between the first transition surface 148 and thecentral axis 150 (see FIG. 2) may be between about 50° and about 70°(e.g., about 60°).

A radius of curvature R₂ of an outer surface of the bumps 164 may be,for example, between about 0.02 inch and about 0.13 inch. Morespecifically, the radius of curvature R₂ of an outer surface of thebumps 164 may be, for example, between about 0.06 inch and about 0.1inch. As a specific, nonlimiting example, the radius of curvature R₂ ofan outer surface of the bumps 164 may be, for example, about 0.08 inch.In some embodiments, each bump 164 may have the same radius of curvatureR. In other embodiments, at least one bump 164 may have a differentradius of curvature R from a radius of curvature of at least one otherbump 164.

FIG. 6 is a perspective view of yet another embodiment of a cuttingelement 170 usable with the earth-boring tool 100 of FIG. 1. As shown inFIG. 6, the curved, stress-reduction feature 156 may include a waveform174 formed in a second transition surface 172. More specifically, thesecond transition surface 172 may extend from the first transitionsurface 148 to an undulating edge 176 at a longitudinally uppermostextent of the second transition surface 172 farthest from the substrate132. The undulating edge 176 may exhibit, for example, a sinusoidalshape. A surface 178 of the waveform 174 may extend from the undulatingedge 176 radially inward toward the central axis 150. The surface 178 ofthe waveform 174 may also extend longitudinally from the undulating edge176 toward the substrate 132, such that the surface 178 extends in athird direction oblique to the central axis 150. More specifically, thetroughs of the waveform 174 may extend in a radial directionperpendicular to the central axis 150, and the peaks of the waveform 174may extend in a radial direction oblique to the central axis 150, suchthat the height of the peaks decreases as radial distance from thecentral axis 150 decreases. In addition to inducing beneficial stressstates within the cutting element 170, the waveform 174 may increasefluid flow across the polycrystalline, superabrasive material 134,improving cooling and facilitating removal of cuttings.

The surface 178 of the waveform 174 may intersect with a planar surface180 extending perpendicular to, and intersected by, the central axis150. The planar surface 180 may be located, for example, in the sameposition along the longitudinal axis 150 as the edge defined at theintersection between the first transition surface 148 and the secondtransition surface 172. A diameter d of the planar surface 180 may be,for example, between about 10% and about 50% of a maximum diameterd_(max) of the polycrystalline, superabrasive material 134. Morespecifically, the diameter d of the planar surface 180 may be, forexample, between about 20% and about 40% of the maximum diameter d_(max)of the polycrystalline, superabrasive material 134. As a specific,nonlimiting example, the diameter d of the planar surface 180 may be,for example, between about 25% and about 35% (e.g., about 30%) of themaximum diameter d_(max) of the polycrystalline, superabrasive material134. In some embodiments, the planar surface 180 may exhibit a differentdegree of roughness than a remainder of the exposed surfaces of thepolycrystalline, superabrasive material 134. For example, the planarsurface 180 may be rougher than (e.g., may be polished to a lesserdegree or with a less fine polish) the remainder of the exposed surfacesof the polycrystalline, superabrasive material 134. The change indirection from the surface 178 of the waveform 174 to the planar surface180, and the optional change in roughness in certain embodiments, maycause cuttings produced by the cutting element 170 to break off, actingas a chip breaker.

A frequency of the waveform 174 may be, for example, between about onepeak every 180° and about ten peaks every 90°. More specifically, thefrequency of the waveform 174 may be, for example, between about twopeaks every 90° and about eight peaks every 90°. As a specific,nonlimiting example, the frequency of the waveform 174 may be, forexample, between about three peaks every 90° and about seven peaks every90° (e.g., about five peaks every 90°).

In embodiments where the cutting element 170 includes a waveform 174,such as that shown in FIG. 6, the first portion of the cutting element170 to contact an underlying earth formation may be the peak or peaks ofthe waveform 174 that are being forced into the earth formation byapplied weight on the earth-boring tool 100 (see FIG. 1). As a result,the surface area that initially contacts the earth formation may bereduced, which may increase the stress induced in the earth formation tobetter initiate and propagate cracks therein.

Various features of the cutting elements shown in FIGS. 2 through 6 maybe combined with one another. For example, cutting elements inaccordance with this disclosure may include the curved second transitionsurface 152 of FIGS. 2 and 3 in combination with the bumps 164 of FIGS.4 and 5, the waveform 174 of FIG. 6, or both. As another example,cutting elements in accordance with this disclosure may include thebumps 164 of FIGS. 4 and 5 in combination with the curved secondtransition surface 152 of FIGS. 2 and 3, the waveform 174 of FIG. 6, orboth.

FIG. 7 is partial cutaway perspective view of still another embodimentof a cutting element 210 usable with the earth-boring tool 100 ofFIG. 1. In some embodiments, such as that shown in FIG. 7, a surface 212of a waveform 214 may extend longitudinally from the undulating edge 176away from the substrate 132, such that the surface 212 extends in afourth direction oblique to the central axis 150. More specifically, thepeaks of the waveform 214 may extend in a radial direction perpendicularto the central axis 150, and the troughs of the waveform 214 may extendin a radial direction oblique to the central axis 150, such that thedepth of the troughs decreases as radial distance from the central axis150 decreases.

FIG. 8 is a cross-sectional side view of a container 190 usable forforming cutting elements 130, 160, and 170 in accordance with thisdisclosure. The container 190 may include an innermost cup-shaped member192, a mating cup-shaped member 194, and an outermost cup-shaped member196, which may be assembled and swaged and/or welded together to formthe mold container 190. One or more of the cup-shaped members 192, 194,and 196 may include an inverse 198 of the curved, stress-reductionfeature 156 to be formed on the second transition surface 152, 162, 172.For example, the innermost cup-shaped member 192 shown in FIG. 8 mayinclude an inverse 198 of the waveform 174 shown in FIG. 6 or thewaveform 214 shown in FIG. 7.

When forming the cutting element 130, 160, or 170, particles 200 of thesuperabrasive material may be positioned in the container 190 adjacentto the inverse 198. Catalyst material may be positioned in the containerwith the particles 200 of the superabrasive material, such as, forexample, by intermixing particles of the catalyst material with theparticles 200 of the superabrasive material or positioning a mass (e.g.,a foil) of the catalyst material adjacent to the particles 200 of thesuperabrasive material. A preformed substrate or substrate precursormaterial or materials 202 may be positioned in the container 190proximate the particles 200 of the superabrasive material. The container190 may then be closed, and the entire assembly may be subjected to heatand pressure to sinter the particles 200 of the superabrasive material,forming the polycrystalline, superabrasive material 134 (see FIGS. 2-7)and securing it to the substrate 132 (see FIGS. 2-7).

As a result of the curved, stress-reduction features 156 shown herein,the stress, and particularly the occurrence of tensile stress, withinthe cutting elements 130, 160, 170, and 210 may be reduced. For example,the inventors have modeled the stresses experienced by at least one ofthe cutting elements 130, 160, 170, and 210, and the curved,stress-reduction features 156 may reduce the peak tensile stress withinthe cutting elements 130, 160, 170, and 210 by at least 15%. Morespecifically, the curved, stress-reduction features 156 may reduce thepeak tensile stress by between about 15% and about 50%. As a specific,nonlimiting example, the curved, stress-reduction features 156 mayreduce the peak tensile stress by between about 25% and about 45% (e.g.,about 30%). It is expected that the others of the cutting elements 130,160, 170, and 210 will perform similarly to, if not better than, thesimulated results.

Additional, nonlimiting embodiments within the scope of this disclosureinclude the following:

Embodiment 1: A cutting element for an earth-boring tool, comprising: asubstrate; and a polycrystalline, superabrasive material secured to anend of the substrate, the polycrystalline, superabrasive materialcomprising: a first transition surface extending in a direction obliqueto a central axis of the substrate; a second transition surfaceextending in a second direction oblique to the central axis, the seconddirection being different from the first direction; and a curved,stress-reduction feature located on the second transition surface.

Embodiment 2: The cutting element of Embodiment 1, wherein the curved,stress-reduction feature comprises a radiusing of the second transitionsurface, such that a slope of the second transition surface changescontinuously from the first transition surface to a cutting face of thepolycrystalline, superabrasive material extending perpendicular to thecentral axis.

Embodiment 3: The cutting element of Embodiment 2, wherein a radius ofcurvature of the second transition surface is between 0.042 inch and0.13 inch.

Embodiment 4: The cutting element of Embodiment 1, wherein the curved,stress-reduction feature comprises protrusions extending outward fromthe second transition surface.

Embodiment 5: The cutting element of Embodiment 4, wherein theprotrusions are positioned in a repeating pattern around a circumferenceof the second transition surface at a frequency of between one every 90°and ten every 90°.

Embodiment 6: The cutting element of Embodiment 4 or Embodiment 5,wherein a perimeter of each protrusion as viewed in a plane at leastsubstantially normal to the second transition surface at a geometricalcenter of a respective protrusion is circular.

Embodiment 7: The cutting element of Embodiment 1, wherein the curved,stress-reduction feature comprises a waveform extending around acircumference of the second transition surface.

Embodiment 8: The cutting element of Embodiment 7, wherein a surface ofthe waveform positioned to engage with an underlying earth formation andextending radially from the second transition surface toward the centralaxis is tapered toward the substrate.

Embodiment 9: The cutting element of Embodiment 8, wherein the surfaceof the waveform extends from the second transition surface to a planarsurface of the polycrystalline, superabrasive material, the planarsurface oriented perpendicular, and located proximate, to the centralaxis.

Embodiment 10: The cutting element of any one of Embodiments 7 through9, wherein a frequency of the waveform is between one every 180° and tenevery 90°.

Embodiment 11: The cutting element of any one of Embodiments 1 through10, wherein a maximum thickness of the second transition surface asmeasured in a direction parallel to the central axis is between 0.01inch and 0.05 inch.

Embodiment 12: An earth-boring tool, comprising: a body; and a cuttingelement secured to the body, the cutting element comprising: asubstrate; and a polycrystalline, superabrasive material secured to anend of the substrate, the polycrystalline, superabrasive materialcomprising: a first transition surface extending in a direction obliqueto a central axis of the substrate; a second transition surfaceextending in a second direction oblique to the central axis, the seconddirection being different from the first direction; and a curved,stress-reduction feature located on the second transition surface.

Embodiment 13: The cutting element of Embodiment 12, wherein the curved,stress-reduction feature comprises a radiusing of the second transitionsurface, such that a slope of the second transition surface changescontinuously from the first transition surface to a cutting face of thepolycrystalline, superabrasive material extending perpendicular to thecentral axis.

Embodiment 14: The cutting element of Embodiment 13, wherein a radius ofcurvature of the second transition surface is between 0.042 inch and0.13 inch.

Embodiment 15: The cutting element of Embodiment 12, wherein the curved,stress-reduction feature comprises protrusions extending outward fromthe second transition surface.

Embodiment 16: The cutting element of Embodiment 15, wherein theprotrusions are positioned in a repeating pattern around a circumferenceof the second transition surface at a frequency of between one every 90°and ten every 90°.

Embodiment 17: The cutting element of Embodiment 15 or Embodiment 16,wherein a perimeter of each protrusion as viewed in a plane at leastsubstantially normal to the second transition surface at a geometricalcenter of a respective protrusion is circular.

Embodiment 18: The cutting element of Embodiment 12, wherein the curved,stress-reduction feature comprises a waveform extending around acircumference of the second transition surface.

Embodiment 19: The cutting element of Embodiment 18, wherein a surfaceof the waveform positioned to engage with an underlying earth formationand extending radially from the second transition surface toward thecentral axis is tapered toward the substrate.

Embodiment 20: The cutting element of Embodiment 19, wherein the surfaceof the waveform extends from the second transition surface to a planarsurface of the polycrystalline, superabrasive material, the planarsurface oriented perpendicular, and located proximate, to the centralaxis.

Embodiment 21: The cutting element of any one of Embodiments 18 through20, wherein a frequency of the waveform is between one every 180° andten every 90°.

Embodiment 22: The cutting element of any one of Embodiments 12 through21, wherein a maximum thickness of the second transition surface asmeasured in a direction parallel to the central axis is between 0.01inch and 0.05 inch.

Embodiment 23: A method of making a cutting element for an earth-boringtool, comprising: shaping a polycrystalline, superabrasive material tocomprise: a first transition surface extending in a direction oblique toa central axis of the substrate; a second transition surface extendingin a second direction oblique to the central axis, the second directionbeing different from the first direction; and a curved, stress-reductionfeature located on the second transition surface; and securing thepolycrystalline, superabrasive material to a substrate.

Embodiment 24: The method of Embodiment 23, wherein shaping thepolycrystalline, superabrasive material comprises positioning aprecursor material into a container exhibiting an inverse of a finalshape of the polycrystalline, superabrasive material and sintering theprecursor material to form the polycrystalline, superabrasive material.

Embodiment 25: The method of Embodiment 23 or Embodiment 24, whereinshaping the polycrystalline, superabrasive material to comprise thecurved, stress-reduction feature comprises shaping the polycrystalline,superabrasive material to comprise a radiusing of the second transitionsurface, such that a slope of the second transition surface changescontinuously from the first transition surface to a cutting face of thepolycrystalline, superabrasive material extending perpendicular to thecentral axis.

Embodiment 26: The method of Embodiment 23 or Embodiment 24, whereinshaping the polycrystalline, superabrasive material to comprise thecurved, stress-reduction feature comprises shaping the polycrystalline,superabrasive material to comprise protrusions extending outward fromthe second transition surface.

Embodiment 27: The method of Embodiment 23 or Embodiment 24, whereinshaping the polycrystalline, superabrasive material to comprise thecurved, stress-reduction feature comprises shaping the polycrystalline,superabrasive material to comprise a waveform extending around acircumference of the second transition surface.

Embodiment 28: The method of Embodiment 27, shaping the polycrystalline,superabrasive material to comprise the waveform comprises tapering asurface of the waveform toward the substrate, the surface of thewaveform positioned to engage with an underlying earth formation andextending radially from the second transition surface toward the centralaxis.

Embodiment 29: The method of Embodiment 28, wherein tapering the surfaceof the waveform comprises tapering the surface of the waveform to extendfrom the second transition surface to a planar cutting face of thepolycrystalline, superabrasive material, the planar cutting faceoriented perpendicular, and located proximate, to the central axis.

Embodiment 30: The method of any one of Embodiments 23 through 29,wherein shaping the polycrystalline, superabrasive material to comprisethe second transition surface comprises rendering a maximum thickness ofthe second transition surface as measured in a direction parallel to thecentral axis between 0.01 inch and 0.05 inch.

While certain illustrative embodiments have been described in connectionwith the figures, those of ordinary skill in the art will recognize andappreciate that the scope of this disclosure is not limited to thoseembodiments explicitly shown and described in this disclosure. Rather,many additions, deletions, and modifications to the embodimentsdescribed in this disclosure may be made to produce embodiments withinthe scope of this disclosure, such as those specifically claimed,including legal equivalents. In addition, features from one disclosedembodiment may be combined with features of another disclosed embodimentwhile still being within the scope of this disclosure, as contemplatedby the inventor.

What is claimed is:
 1. A cutting element for an earth-boring tool,comprising: a polycrystalline, superabrasive material secured to an endof a substrate, the polycrystalline, superabrasive material comprising:a first transition surface located proximate to a periphery of thepolycrystalline, superabrasive material, the first transition surfaceextending oblique to a central axis of the substrate; a secondtransition surface located adjacent to the first transition surface, thesecond transition surface extending oblique to the central axis; and asurface of a waveform extending around a circumference of the secondtransition surface, the surface of the waveform tapered toward thesubstrate and extending radially from the second transition surfacetoward the central axis, the surface of the waveform extending from thesecond transition surface to a planar surface of the polycrystalline,superabrasive material located at a same distance from the substrate astroughs of the waveform surface, the planar surface orientedperpendicular, and located proximate, to the central axis.
 2. Thecutting element of claim 1, wherein a frequency of the waveform isbetween one every 180° and ten every 90°.
 3. The cutting element ofclaim 1, wherein a maximum thickness of the second transition surface asmeasured in a direction parallel to the central axis is between 0.01inch and 0.05 inch.
 4. The cutting element of claim 1, wherein thesecond transition surface is curved.
 5. The cutting element of claim 1,wherein peaks of the waveform are positioned to contact an underlyingearth formation before any other portion of the polycrystalline,superabrasive material.
 6. The cutting element of claim 1, wherein aroughness of the planar surface is different from a roughness of otherexposed surfaces of the polycrystalline, superabrasive material.
 7. Thecutting element of claim 6, wherein the planar surface is rougher thanthe other exposed surfaces of the polycrystalline, superabrasivematerial.
 8. The cutting element of claim 1, wherein a diameter of theplanar surface is between 10% and 50% of a maximum diameter of thepolycrystalline, superabrasive material.
 9. The cutting element of claim1, wherein a shape of the second transition surface between the firsttransition surface and the waveform is sinusoidal.
 10. The cuttingelement of claim 1, wherein the waveform is configured to reduce peaktensile stress within the polycrystalline, superabrasive material bybetween about 15% and about 50%.
 11. An earth-boring tool, comprising: abody; and a cutting element secured to the body, the cutting elementcomprising: a polycrystalline, superabrasive material secured to an endof a substrate, the polycrystalline, superabrasive material comprising:a first transition surface located proximate to a periphery of thepolycrystalline, superabrasive material, the first transition surfaceextending oblique to a central axis of the substrate; a secondtransition surface located adjacent to the first transition surface, thesecond transition surface extending oblique to the central axis; and asurface of a waveform extending around a circumference of the secondtransition surface, the surface of the waveform tapered toward thesubstrate and extending radially from the second transition surfacetoward the central axis, the surface of the waveform extending from thesecond transition surface to a planar surface of the polycrystalline,superabrasive material located at a same distance from the substrate astroughs of the waveform surface, the planar surface orientedperpendicular, and located proximate, to the central axis.
 12. Theearth-boring tool of claim 11, wherein a frequency of the waveform isbetween one every 180° and ten every 90°.
 13. The earth-boring tool ofclaim 11, wherein a maximum thickness of the second transition surfaceas measured in a direction parallel to the central axis is between 0.01inch and 0.05 inch.
 14. The earth-boring tool of claim 11, wherein thesecond transition surface is curved.
 15. The earth-boring tool of claim11, wherein a roughness of the planar surface is different from aroughness of other exposed surfaces of the polycrystalline,superabrasive material.
 16. The cutting element of claim 11, wherein adiameter of the planar surface is between 10% and 50% of a maximumdiameter of the polycrystalline, superabrasive material.
 17. A method ofremoving an earth formation, comprising: rotating a body of anearth-boring tool; and removing an earth material in contact with apolycrystalline, superabrasive material of a cutting element secured tothe body, the polycrystalline, superabrasive material comprising: afirst transition surface located proximate to a periphery of thepolycrystalline, superabrasive material, the first transition surfaceextending oblique to a central axis of a substrate; a second transitionsurface located adjacent to the first transition surface, the secondtransition surface extending oblique to the central axis; and a waveformextending around a circumference of the second transition surface, asurface of the waveform tapered toward from the substrate and extendingradially from the second transition surface toward the central axis, thesurface of the waveform extending from the second transition surface toa planar surface of the polycrystalline located at a same distance fromthe substrate as troughs of the waveform surface, the planar surfaceoriented perpendicular, and located proximate, to the central axis. 18.The method of claim 17, wherein removing the earth material in contactwith the polycrystalline, superabrasive material comprises contactingthe earth material with peaks of the waveform before any other portionof the polycrystalline, superabrasive material.
 19. The method of claim17, further comprising mitigating tensile stress within thepolycrystalline, superabrasive material utilizing the waveform.
 20. Themethod of claim 17, further comprising breaking a chip of the earthmaterial when the earth material reaches an intersection between thewaveform and the planar surface.